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The expected node-independence number of random trees

โœ Scribed by A Meir; J.W Moon


Publisher
Elsevier Science
Year
1973
Weight
289 KB
Volume
76
Category
Article
ISSN
1385-7258

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Let (Y(G~,~) denote the independence number of the random graph Gn,p. Let d = np. We show that if E > 0 is fixed then with probability going to 1 as n + m cu(G& -$t (log d -log log dlog 2 + 1) < 7 provided d, s d = o(n), where d, is some fixed constant.

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Let Qn.k,, be the number of all n-node ordered trees with r nodes of maximum level k and let B,,\*,, be the number of all r-tuply rooted ordered trees with n nodes and height less than or equal to k. In this paper we derive the identitity where n, k, r > 0. An explicit expression for Qn,k,r and its